Stable standing waves for a Schrödinger system with nonlinearχ3 response

In this paper, we consider standing waves for a nonlinear Schrödinger system which appears in nonlinear optics. This two-component system contains a cubic nonlinear term which is called χ3-interaction, and has a strong coupling on one side only. Oliveira and Pastor [Anal. Math. Phys. 11, 123 (2021)] showed the existence of ground states solutions for the corresponding stationary problems and investigated their stability. In our study, by considering the solvability of a constraint minimization problem, we show the existence of stable standing wave solutions. We also investigate the correspondence between minimizers and ground state solutions.